This paper deals with an inventory problem in multilocation supply systems. We minimize the one-period expected costs. I t is shown, that for more than two locations the problem is not solvable in the framework of our model. Constraints for the costparameters are also obtained. This dlowes t o solve the problem of an optimal redistribution of the present stock among all locations as a transportation problem of linear programming. Some assertions about the optimal inventory policy are made. The two-location supply system in detail is considered.